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Recently, a chaotic image encryption algorithm based on information entropy (IEAIE) was proposed. This paper scrutinizes the security properties of the algorithm and evaluates the validity of the used quantifiable security metrics. When the round number is only one, the equivalent secret key of every basic operation of IEAIE can be recovered with a differential attack separately. Some common insecurity problems in the field of chaotic image encryption are found in IEAIE, e.g. the short orbits of the digital chaotic system and the invalid sensitivity mechanism built on information entropy of the plain image. Even worse, each security metric is questionable, which undermines the security credibility of IEAIE. Hence, IEAIE can only serve as a counterexample for illustrating common pitfalls in designing secure communication method for image data.

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Chaotic dynamics is an important source for generating pseudorandom binary sequences (PRNS). Much efforts have been devoted to obtaining period distribution of the generalized discrete Arnold's Cat map in various domains using all kinds of theoretical methods, including Hensel's lifting approach. Diagonalizing the transform matrix of the map, this paper gives the explicit formulation of any iteration of the generalized Cat map. Then, its real graph (cycle) structure in any binary arithmetic domain is disclosed. The subtle rules on how the cycles (itself and its distribution) change with the arithmetic precision e are elaborately investigated and proved. The regular and beautiful patterns of Cat map demonstrated in a computer adopting fixedpoint arithmetics are rigorously proved and experimentally verified. The results will facilitate research on dynamics of variants of the Cap map in any domain and its effective application in cryptography. In addition, the used methodology can be used to evaluate randomness of PRNS generated by iterating any other maps.